How to join two bones that are part of the same armature
FILE BLEND



Here some shots of the final result





In order 

1) In Edit Mode I select boneA and press alt + f in order to switch its direction (as you can see is the only bone having the opposite direction respect the others bone of the tail of your bird)

PS remember when you use alt + f your bone will switch direction AND will lose every connection with the other bones; for this reason i will do step number 4) and number 5)

2) I take the boneA and i move its "head" near to the tail of boneB 

3) Now I follow the step i tell you before:  select boneB - press shift - select boneA (remember the order is important); in this way you'll have both bones selected.

4) Press Ctrl + P and click Connected

5) In the end to keep your boneA connected with your bird's tail (i.e. the boneC and the others) i add a Copy Location in boneA